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But the Prime Minister said: “You can debate these things for the future but the important thing at the moment is I don't really think people want me to be obsessed with the constitutional issue this month or next month.

“I think what they want us to do is concentrate on making sure the economy comes through recession.”

The Government will shortly announce its response to the Calman Commission on devolution, which recommended a swathe of new powers be transferred to Holyrood.

Mr Salmond, the First Minister, has offered to include the recommendations in a three-option referendum, alongside the status quo and full independence.

Labour’s bloc of MSPs would give the minority SNP administration at Holyrood the support it needs to stage a vote. However, Mr Murphy has rejected the First Minister’s offer.

Asked if he could see a time when a future Labour Government offered a referendum to settle Scotland's constitutional future, Mr Brown replied: “Of course that's a possibility.

“The Calman report recommends new devolution arrangements, and obviously these are big changes that will make devolution work better. But they are not separation.”

Defending Labour’s opposition to holding a referendum now, he said it was “absolutely right” to take this stance during a recession.

But Kenny Gibson, a SNP backbench MSP, said: “This is a significant move by Gordon Brown since he has never conceded the principle of an independence referendum until now.”

He argued there was no reason not to stage a vote next year, as by then Scotland will be moving out of recession.

Labour’s opposition to a referendum was set in stone until the middle of last year when Wendy Alexander, Mr Gray’s predecessor, challenged the SNP to “bring it on”.

After Mr Gray succeeded her last autumn, the party reverted to opposing a referendum, claiming the separatists had run away from a vote when she gave them the chance.

However, Mr Gray used his conference speech to say “the day may well come” for a referendum, and Mr Murphy said it would be considered “at some point in the future”.